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図書

図書
edited by David Chillingworth
出版情報: Berlin ; New York : Springer-Verlag, 1971  x, 173 p ; 26 cm
シリーズ名: Lecture notes in mathematics ; 206
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2.

図書

図書
Michel Demazure ; translated from the French by David Chillingworth
出版情報: Berlin ; Tokyo : Springer, c2000  viii, 301 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Introduction
Notation
Local Inversion / 1:
A Preliminary Statement / 1.1:
Partial Derivatives. Strictly Differentiable Functions / 1.3:
The Local Inversion Theorem: General Statement / 1.4:
Functions of Class Cr / 1.5:
The Local Inversion Theorem for Cr maps / 1.6:
Generalizations of the Local Inversion Theorem / 1.8:
Submanifolds / 2:
Definitions of Submanifolds / 2.1:
First Examples / 2.3:
Tangent Spaces of a Submanifold / 2.4:
Transversality: Intersections / 2.5:
Transversality: Inverse Images / 2.6:
The Implicit Function Theorem / 2.7:
Diffeomorphisms of Submanifolds / 2.8:
Parametrizations, Immersions and Embeddings / 2.9:
Proper Maps: Proper Embeddings / 2.10:
From Submanifolds to Manifolds / 2.11:
Some History / 2.12:
Transversality Theorems / 3:
Countability Properties in Topology / 3.1:
Negligible Subsets / 3.3:
The Complement of the Image of a Submanifold / 3.4:
Sard''s Theorem / 3.5:
Critical Points, Submersions and the Geometrical Form of Sard''s Theorem / 3.6:
The Transversality Theorem: Weak Form / 3.7:
Jet Spaces / 3.8:
The Thom Transversality Theorem / 3.9:
Classification of Differentiable Functions / 3.10:
Taylor Formulae Without Remainder / 4.1:
The Problem of Classification of Maps / 4.3:
Critical Points: the Hessian Form / 4.4:
The Morse Lemma / 4.5:
Fiburcations of Critical Points / 4.6:
Apparent Contour of a Surface in R3 / 4.7:
Maps from R2 into R2 / 4.8:
Envelopes of Plane Curves / 4.9:
Caustics / 4.10:
Genericity and Stability / 4.11:
Catastrophe Theory / 5:
The Language of Germs / 5.1:
r-sufficient Jets; r-determined Germs / 5.3:
The Jacobian Ideal / 5.4:
The Theorem on Sufficiency of Jets / 5.5:
Deformations of a Singularity / 5.6:
The Principles of Catastrophe Theory / 5.7:
Catastrophes of Cusp Type / 5.8:
A Cusp Example / 5.9:
Liquid-Vapour Equilibrium / 5.10:
The Elementary Catastrophes / 5.11:
Catastrophes and Controversies / 5.12:
Vector Fields / 6:
Exemples of Vector Fields (Rn Case) / 6.1:
First Integrals / 6.3:
Vector Fields on Submanifolds / 6.4:
The Uniqueness Theorem and Maximal Integral Curves / 6.5:
One-parameter Groups of Diffeomorphisms / 6.6:
The Existence Theorem (Local Case) / 6.8:
The Existence Theorem (Global Case) / 6.9:
The Integral Flow of a Vector Field / 6.10:
The Main Features of a Phase Portrait / 6.11:
Discrete Flows and Continuous Flows / 6.12:
Linear Vector Fields / 7:
The Spectrum of an Endomorphism / 7.1:
Space Decomposition Corresponding to Partition of the Spectrum / 7.3:
Norm and Eigenvalues / 7.4:
Contracting, Expanding and Hyperbolic Endommorphisms / 7.5:
The Exponential of an Endomorphism / 7.6:
One-parameter Groups of Linear Transformations / 7.7:
The Image of the Exponential / 7.8:
Contracting, Expanding and Hyperbolic Exponential Flows / 7.9:
Topological Classification of Linear Vector Fields / 7.10:
Topological Classification of Automorphisms / 7.11:
Classification of Linear Flows in Dimension 2 / 7.12:
Singular Pints of Vector Fields / 8:
The Classification Problem / 8.1:
Linearization of a Vector Field in the Neighbourhodd of a Singular Point / 8.3:
Difficulties with Linearization / 8.4:
Singularities with Attracting Linearization / 8.5:
Liapunov Theory / 8.6:
The Theorems of Grobman and Hartman / 8.7:
Stable and Unstable Manifolds of a Hyperbolic Singularity / 8.8:
Differentiable Linearization: Statement of the Problem / 8.9:
Differentiable Linearization: Resonances / 8.10:
Differentiable Linearization: The Theorems of Sternberg and Hartman / 8.11:
Linearization in Dimenension 2 / 8.12:
Some Historical Landmarks / 8.13:
Closed Orbits - Structural Stability / 9:
The Poincarè Map / 9.1:
Characteristic Multipliers of a Closed Orbit / 9.3:
Attracting Closed Orbits / 9.4:
Classification of Closed Orbits and Classification of Diffeomorphisms / 9.5:
Hyperbolic Closed Orbits / 9.6:
Local Structural Stability / 9.7:
The Kupka-Smale Theorem / 9.8:
Morse-Smale Fields / 9.9:
Structural Stability Through the Ages / 9.10:
Bifurcations of Phase Portrait / 10:
What Do We Mean by a Bifurcation? / 10.1:
The Centre Manifold Theorem / 10.3:
The Saddle-Node Bifurcation / 10.4:
The Hopf Bifurcation / 10.5:
Local Bifurcations Carried by a Closed Orbit / 10.6:
Saddle / 10.7:
Introduction
Notation
Local Inversion / 1:
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